Abstract
The Harary index (HI), the average distance (AD), the Wiener polarity index (WPI) and the connective eccentricity index (CEI) are distance-based graph invariants, some of which found applications in chemistry. We investigate the relationship between HI, AD, and CEI, and between WPI, AD, and CEI. First, we prove that HI > AD for any connected graph and that HI > CEI for trees, with only three exceptions. We compare WPI with CEI for trees, and give a classification of trees for which CEI ? WPI or CEI < WPI. Furthermore, we prove that for trees, WPI > AD, with only three exceptions.
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